Not sure if this was intended to be rhetorical, but a big part of what makes turbulence difficult is that we see eddies at many scales, including very small eddies (at least down to the scale that Navier-Stokes holds). I remember a striking graphic about the onset of turbulence in a pot of boiling water, in which the eddies repeatedly halve in size as certain parameter cutoffs are passed, and the number of eddies eventually diverges—that’s the onset of turbulence.
Sorry for being unclear – it was definitely not intended to be rhetorical!
Yes, turbulence was exactly what I was thinking about. At some small enough scale, we probably wouldn’t expect to ‘find’ or be able to distinguish eddies. So there’s probably some minimum size. But then is there any pattern or structure to the larger sizes of eddies? For (an almost certainly incorrect) example, maybe all eddies are always a multiple of the minimum size and the multiple is always an integer power of two. Or maybe there is no such ‘discrete quantization’ of eddy sizes, tho eddies always ‘split’ into nested halves (under certain conditions).
It certainly seems the case tho that eddies aren’t possible as emergent phenomena at a scale smaller than the discretization of the approximation itself.
Not sure if this was intended to be rhetorical, but a big part of what makes turbulence difficult is that we see eddies at many scales, including very small eddies (at least down to the scale that Navier-Stokes holds). I remember a striking graphic about the onset of turbulence in a pot of boiling water, in which the eddies repeatedly halve in size as certain parameter cutoffs are passed, and the number of eddies eventually diverges—that’s the onset of turbulence.
Sorry for being unclear – it was definitely not intended to be rhetorical!
Yes, turbulence was exactly what I was thinking about. At some small enough scale, we probably wouldn’t expect to ‘find’ or be able to distinguish eddies. So there’s probably some minimum size. But then is there any pattern or structure to the larger sizes of eddies? For (an almost certainly incorrect) example, maybe all eddies are always a multiple of the minimum size and the multiple is always an integer power of two. Or maybe there is no such ‘discrete quantization’ of eddy sizes, tho eddies always ‘split’ into nested halves (under certain conditions).
It certainly seems the case tho that eddies aren’t possible as emergent phenomena at a scale smaller than the discretization of the approximation itself.